Question

Two strings are of equal length. The one with the smaller cross section has a diameter of 0.7 mm and is under 660 N of tension. The second string has double the radius of the first and is under twice the tension. Find the ratio of the wave speed in the strings, expressed as a ratio of higher speed over lower speed.

Answer 1

wave speed of string is given as

where is mass per unit length.

Now, as the lengths are equal, taking mass as volume times density,

Assuming the strings to be of same material, so same density, and lengths are given to be equal. Therefore,

and

Thus, the ratio is